Total Least Squares Phase Retrieval

TL;DR

This paper introduces a total least squares approach to phase retrieval that accounts for errors in sensing vectors, providing a more accurate and efficient solution demonstrated through simulations and real optical hardware experiments.

Contribution

It extends phase retrieval methods to handle sensing vector errors using TLS, deriving gradients and error conditions for improved accuracy.

Findings

TLS-based phase retrieval outperforms LS in the presence of sensing vector errors

The method is computationally simple and efficient using gradient descent

Experimental results on optical hardware validate the approach

Abstract

We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this approach to handle errors in the sensing vectors by adopting the total least squares (TLS) framework that is used in linear inverse problems with operator errors. We show how gradient descent and the specific geometry of the phase retrieval problem can be used to obtain a simple and efficient TLS solution. Additionally, we derive the gradients of the TLS and LS solutions with respect to the sensing vectors and measurements which enables us to calculate the solution errors. By analyzing these error expressions we determine conditions under which each method should outperform the other. We run simulations to demonstrate that our method can lead to more accurate solutions. We further demonstrate the effectiveness of our approach by performing phase retrieval experiments on real optical hardware which naturally contains both sensing vector and measurement errors.